Using change in the white share of the population as an admittedly crude proxy, Petrilli identifies the 25 ZIP codes in the U.S. that saw the largest change in the white share of the population between 2000 and 2010. And, as he notes, some of the cities housing these ZIP codes were a bit surprising to see.

I’m not an expert on gentrification (education policy is my beat) but I was surprised by the list. I expected to see Chicago, Brooklyn, Washington, D.C., and Denver. But Chattanooga? Columbia, SC? Oklahoma City? St. Louis? This is not a phenomenon limited to a few of our great coastal cities. These gentrifying neighborhoods are literally all over the map.

Indeed, Columbia, South Carolina, shows up at the top of this list, with a single ZIP code that recorded 47.1 percent change in the white share of the population. However, it turns out the ZIP code in question – 29202 – is for post office boxes only, so it's unlikely that change is the result of gentrification.

But the location of nearly every other ZIP in the list does show us something: They're pretty much all located in the hearts of their cities' downtowns. These are parts of cities that have seen increased attention from housing developers and both renters and buyers in recent years. With more housing now available in downtowns, their populations are increasing.

The 24011 ZIP in Roanoke, Virginia, for example, ranks fourth on the list (third if you take out the P.O. box-only ZIP from Columbia) and saw a 34.9 percent increase in its share of white people between 2000 and 2010. That ZIP code had a population of 219 people in 2010.

24011 is right in the heart of downtown, according to Sean Luther, president and CEO of the non-profit Downtown Roanoke Incorporated. He says that more and more people are moving to that part of the city, but it's not exactly gentrification so much as simple growth.

"Our ZIP codes have not gone from heavily minority to heavily white, they've gone from zero to people. We're not an example of gentrification so much as the introduction of residents into a downtown area," Luther says. "We were an industrial downtown and have interjected a residential component as part of an overall resurgence of the downtown."

He says that there's been a number of new housing developments opening downtown, bringing the population there to about 1,100 people according to a survey his organization conducted last fall. However, in a survey of the roughly 400 households downtown, 96 percent of respondents were white, and 50 percent had at least a Bachelor's degree. (The survey had a 20 percent response rate.)

Petrilli also notes that the comparison of ZIP code-based data is also problematic, due to the fact that ZIP codes are regularly altered to meet the Postal Service's needs. So while this may not be the most precise or comprehensive list of gentrification (itself a term not easily defined), this list does offer some helpful information about the demographic shifts in American downtowns. Increasing white populations in these downtown ZIP codes might not necessarily mean gentrification, but it doesn't mean nothing.